ARTICLE pubs.acs.org/JPCC
Plasmon Resonance of Isolated Gold Hollow Nanoparticles and Nanoparticle Pairs: Insights from Electronic Structure Calculations Huili Ma,† Fang Gao,‡ and WanZhen Liang*,† †
Hefei National Laboratory for Physical Science at Microscale, and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China ‡ Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei 230031, China ABSTRACT: Because the feature sizes of noble metal nanoparticles (NPs) are smaller than a few of nanometers, simulations including quantum effects and atomistic details are inevitable. In this work, we report a detailed electronic structure study on the plasmon resonance of isolated gold hollow nanoparticles (NPs) and NP pairs. The long-range-corrected (LRC) density functional theory (DFT) has been employed. We find that the plasmon resonance of small-size gold NPs is very sensitive to NP sizes and interparticle distances. When the NP’s size changes from Au32 to Au17 , the high-energy absorption maximum blue shifts 50 nm and when the interparticle distance of Au17 NP pairs changes from 1.15 to 0.83 nm, the corresponding blue shift is ∼40 nm. The spectral line width becomes narrower as the NP size increases and the interparticle distance reduces. The insight of how the plasmon-resonance peaks of a NP pair are formed and how they are sensitive to the interparticle separation is revealed by the plots of transition densities and frontier molecular orbitals (MOs) as a function of the interparticle distances. As the two NPs approach near touching contact, they are strongly coupled and a bond-forming step takes place, which is verified by the significant overlap between the unoccupied MOs. The strong coupling between the wave functions results in the electrons to redistribute. As a result, we observe that a large number of electrons are localized in the gap and the nearest neighboring atoms of a closely spaced NP pair. The localized electrons enhance the electromagnetic field in the gap of the NP pair, leading to a pronounced red shift and increasing polarizability for the plasmon-resonance peaks, and many new absorption peaks appeared in low-energy range.
I. INTRODUCTION The noble metal NPs (NPs) have received considerable attention because of their intense surface plasmon resonance and the ability to tune it by changing the size, shape, composition, and dielectric environment of nanostructures. The surface plasmon resonance is formed by the resonant interaction between photon and collective electron charge oscillations in metallic NPs,1 which not only makes NPs possess the brilliant optical properties, but also offers a strongly enhanced near field to enhance spectroscopic signals of the adsorbed molecules.2 7 The noble metal NPs exhibit a strong absorption band in the ultraviolet visible light region that is absent in the bulk metal and is originated from the collective electron charge oscillations. For example, there is a strong absorption band at ∼520 nm for gold NPs with the diameter 22 nm,8,9 whereas the resonance is at ∼440 nm for silver spheres, and the line width is narrower. The quasi-static regime holds when the diameter is in the range of approximately 10 to 50 nm, and the plasmon resonance is nearly independent of the particle size but highly sensitive to the shape of the particle and its embedded media.6,8,10 13 Therefore, a detailed correspondence between the NP structure and its optical response is essential. The modeling and simulation of the optical response of nanostructures provide a detailed, quantitative understanding r 2011 American Chemical Society
of these systems, allowing a close interplay of theory and experiment. Early in the 20th century, it was based on analytical solutions of Maxwell’s equations to address light scattering by NPs of simple geometries, such as spheres and ellipsoids. For spheres, the solutions are known as Mie resonances.14 As the structural complexity of NPs increases, many numerical methods, such as the most commonly used finite difference time domain method,15 the discrete dipole approximation,16,17 the multiple multipole method,18 multiple scattering techniques, transfer matrix approaches19 and finite-element method,20 and so on, have been employed to describe the surface plasmon modes of a variety of structures, including slabs, cylinders, cubes, edges, hemispheres, coupled spheres, and NP arrays. These methods have proven to be immensely useful for interpreting a wide range of nanoscience experiments and providing the capability to describe optical properties of particles up to several hundred nanometers in dimension, with arbitrary particle structures and complex dielectric environments taken into consideration. An overview about these analytical and numerical methods Received: September 29, 2011 Revised: December 15, 2011 Published: December 16, 2011 1755
dx.doi.org/10.1021/jp2094092 | J. Phys. Chem. C 2012, 116, 1755–1763
The Journal of Physical Chemistry C for the description of electromagnetic properties of silver and gold NPs has recently been provided by Schatz’s group.21 However, as the size of metal particles decreases to the Bohr radius of an exciton, the electronic motion becomes confined and the confinement of the charge carrier discretizes the electronic energy band. As a result, the noble-metal NPs with the diameter
